Pathwise Relational Conformer Tensors for Molecular Ensemble Learning

Molecular conformer ensembles are often modeled as sets of three-dimensional structures, yet they possess substantially more structure than generic sets: all conformers share the same molecular graph, inducing exact correspondence among atoms, bonds, angles, and torsions. We argue that these aligned local structures provide natural sites for relational computation before ensemble aggregation. We introduce PaSTNet, a molecular ensemble architecture built around the Pathwise State Tensor (PaST) operator. For each molecular path, PaST lifts conformer path states into channel-valued symmetric and antisymmetric pair tensors, contextualizes these relations using permutation-equivariant tensor operations, and contracts them back into conformer updates. We characterize PaST's linear core and show that its structural maps form complete families of homogeneous permutation-equivariant linear operators within the symmetric and antisymmetric pair branches at fixed conformer cardinality. To center each block's ensemble response relative to a singleton reference, PaST further employs a singleton-centered residual that subtracts the response of the same relational operator re-evaluated on the corresponding singleton input, making each PaST block exactly the identity when only one conformer is available. PaSTNet alternates these relational updates with geometry-conditioned propagation across molecular paths, allowing cross-conformer relational signals induced by conformational differences to propagate through the atom–bond–angle–torsion hierarchy before conformer pooling. Together with reversal-invariant path encoding and invariant geometric descriptors, the resulting model is invariant to a common permutation of conformers, consistent atom relabeling, and independent proper rigid motions of each conformer. Across six molecular property tasks, PaSTNet achieves the best evaluated mean score on five. Identity, attention, pair-local, and no-subtraction controls favor full PaST in mean performance; attribution remains limited by coupled changes in some controls and uncertainty over three splits. PaSTNet therefore provides a principled framework for reasoning explicitly over aligned local relations in molecular conformer ensembles rather than treating conformers only as representations to be pooled.